An Asymptotical $O((k + 1)n^3L)$ Affine Scaling Algorithm for the $P_*(k)$-Matrix Linear Complementarity Problem

Abstract

Based on the generalized Dikin-type direction proposed by Jansen et al in 1997, we give out in this paper a generalized Dinkin-type affine scaling algorithm for solving the $P_*(k)$-matrix linear complementarity problem (LCP). By using high-order correctors technique and rank-one updating, the iteration complexity and the total computational turn out asymptotically $O((\kappa+1)\sqrt{n}L)$ and $O((\kappa+1)n^3L)$ respectively.